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A048111 Number of unitary divisors of n (A034444) < number of non-unitary divisors of n (A048105). 7
16, 32, 36, 48, 64, 72, 80, 81, 96, 100, 108, 112, 128, 144, 160, 162, 176, 180, 192, 196, 200, 208, 216, 224, 225, 240, 243, 252, 256, 272, 288, 300, 304, 320, 324, 336, 352, 360, 368, 384, 392, 396, 400, 405, 416, 432, 441, 448, 450, 464, 468, 480, 484 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n that are expressible as a product of 2 "nonsquarefree" numbers (i.e., there are 2 integers x,y in A001694 such that n = xy). - Benoit Cloitre, Jan 01 2003

Also numbers having more than one square divisor > 1: A046951(a(n)) > 2. - Reinhard Zumkeller, Apr 08 2003

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

A000005(a(n)) > 2^(1 + A001221(a(n))).

EXAMPLE

36 is in the sequence since the number of its unitary divisors, {1, 4, 9, 36} is 4 which is smaller than 5, the number of its non-unitary divisors, {2, 3, 6, 12, 18}.

MATHEMATICA

Select[Range[484], DivisorSigma[0, #] > 2^(PrimeNu[#]+1) &] (* Amiram Eldar, Jun 11 2019 *)

PROG

(PARI) is(n)=my(f=factor(n)[, 2], t); for(i=1, #f, if(f[i]>1, if(t||f[i]>3, return(1), t=1))); 0 \\ Charles R Greathouse IV, Sep 17 2015

CROSSREFS

Cf. A000005, A001221, A034444, A048105, A048109, A082293, A013929, A082294, A082295.

Sequence in context: A296761 A297288 A055075 * A122614 A046101 A044856

Adjacent sequences:  A048108 A048109 A048110 * A048112 A048113 A048114

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified December 9 17:18 EST 2019. Contains 329879 sequences. (Running on oeis4.)